An interesting question! You wouldn't say two French fries, because that would mean just two small pieces of potato: you'd say two portions of fries, or (more casually) two lots of fries. Generally, I'd say the basic rule of countable and non-countable nouns applies: you say 'I'll have a glass of white wine' (countable) but 'I'll have white wine' (non-countable); 'I'll have a chicken sandwich' but 'I'll have chicken'. With non-countable nouns, you'd normally use no article (I'll have cheese souffle) but you might add a definite article (I'll have the Chicken Kiev) - the definite article referring to that particular item on the menu.

I think the answer is different in fast food restaurants compared to fancier restaurants. At McDonald's, it would be normal to say "I'd like a hamburger, a Coke, and two orders of fries." It would sound weird to say "I'd like THE hamburger." But in fancier restaurants, it is normal to say "the" before the name of a dish, like in Giancarlo's example: I'll have the calamaris al ajillo, please. But you would still say I'd like a Coke, not "the" Coke, even in a fancy restaurant.

I'd say yes, if you want to sound proper. You can also use "the". For example, I'll have the calamares al ajillo, please.